Different AIC when using different parameterizations

[Diego.Pavon]

Dear all,

I am running models with covariates. Thus, I am using the alternative parameterization number 3. However when using the other parameterizations, the AIC of the same model changes (sometimes >5 units). Aren't they supposed to have the same AIC since is the same model?

Then, which one should I use? Is there anything wrong with the models? Is perhaps one parameterization better than the other one for this particular case?

Thank you very much.

Diego

[jhines]

Diego,

If you have enough data and the model isn't overparameterized, the 3 parameterizations should give the same results. My guess is that you have a problem with insufficient data for the model, or possibly not enough variation in the covariates. When this happens, I usually look at the results from the model with the lowest value for -2LogLike and use the final estimates from that model as starting values in the other parameterization, after calculating values for the derived beta's for the missing parameters. If you send me the project zipfile, I can show you how it's done.

Jim

[darryl]

What type of model are you trying to run? I'm going to disagree with Jim and say that if you've got covariates in a model then there's no guarantee that different parameterizations will give you the same results depending on what constraints are essentially being forced on parameter values by covariate relationships. Ideally you should be picking the parameterization that makes the most sense to you to answer your questions of interest and not get too worried about the other ones.

Darryl

[jhines]

I agree with Darryl's disagreement I responded without thinking it through. Without covariates, they should produce similar results, but with covariates they usually won't agree.

Jim

[Diego.Pavon]

Hi!

Thanks for the answers!.

The reason why I wanted to try other parameterizations was that I got some convergency problems with the parameterization number 3 (Psi, Eps, p). I am having problems when using covariates in the psi term. Thus, I though about trying other parameterizations and see if I could get some estimates from there and use them as initial values in the parameterization that I wanted (kind of what Jim suggested). When I did so, I found the differences.

Darryl, what I want to see is whether occupancy and (mainly) detectability of mammalian predators are function of food abundance, snow depth, density, location or survey-related covariates such as "days after the last snowfall". I am using data since 1989 (3 surveys (replicates) per year)= Snow track counts. 147 sites from two locations (North and South).

Since I am interested in p and psi, I thought that the 3rd parameterization was the most appropriate. I am having problems of convergence (the program keeps running for long time without giving any results) mainly when constraining psi, already with very simple models (4 parameters), for instance psi(density)eps()p(). I don't find such a problem when constraining extinction or detectability.

Diego

[darryl]

There can be issues with the 2nd and 3rd parameterizations when you start having a number of covariates in the model. What happens is that while trying to find the maximum likelihood estimates for the beta parameters, the software is also checking that all of the probabilities are between 0 and 1, including those that that are derived rather than estimated directly. Otherwise you can find a 'solution' where the estimated probabilities look ok (because of the logit-link function) but derived parameters (in your case colonization) could be outside of 0 an 1 (MARK use to have that issue, not sure if it still does) which just doesn't make sense biologically. Specifying initial starting values can help, and 1 approach there is to start with a simpler model and use the estimates from that model as the starting values for the next model.

If you're not specifically interested in extinction, then you could switch to the 2nd parameterization, and see if that behaves any better.

You could also use the 4th parameterization, although there you are assuming that any changes in occupancy happen essentially at random on the landscape. Which may not be realistic, but if you just want to describe what the pattern of occupancy looked like each year it'll give you an answer.

That said, I often think that the first parameterization is actually most useful for understanding WHY any changes might be occurring rather than WHAT happened, especially from the perspective of future predictions. I also note that you can consider colonization and 1-extinction as occupancy probabilities if you want, we're just allowing those probabilities to be different depending whether the species had been present or absent in the previous time point.

Cheers
Darryl

[Diego.Pavon]

Hi Darryl,

Thank you very much for you answer. Reading your post, I perhaps would like to switch to the first parameterization (in order to understand WHY's). However, I would like to constrain PSI, meaning that I want to see if occupancy is function of an environmental variable (or many) such as food abundance, climate conditions or location. In this case, then, the first parameterization would not be the best option, just because in that case one only estimate initial occupancy and we derive the rest of PSI's, am I right?

Or is it so that we can argue that those variables affecting extinction and colonization are actually affecting occupancy? For instance, if extinction is function of food abundance, then, occupancy would be also function of food abundance. Or am I totally confused?

And if I am not so interested in extinction (or colonization), is it a good idea to put 0's in the column for those parameters to tell the program not to estimate them?

Thank you very much.

Diego